19(T2)28z1xx Chimeric Antigen Receptor (CAR) T Cells in People With B-Cell Cancers

Inclusion Criteria: * Age ≥ 18 years of age * Creatinine ≤2.0 mg/100 ml, direct bilirubin ≤2.0 mg/100 ml, AST and ALT ≤3.0x upper limit of normal (ULN) * Adequate pulmonary function as assessed by ≥92% oxygen saturation on room air by pulse oximetry. * Histologically confirmed DLBCL and large B cell lymphoma, including * DLBCL, not otherwise specified (NOS), or * Transformed DLBCL from follicular lymphoma, or * High-grade B cell lymphoma (excluding Burkitt's lymphoma), or * Primary mediastinal large B cell lymphoma AND * Chemotherapy refractory disease, defined as a failure to achieve at least a partial response or disease progression within 12 months to the last therapy, OR * Disease progression or recurrence in ≤12 months of prior autologous stem cell transplant (ASCT), OR * Relapsed disease after 2 or more prior chemoimmunotherapies with at least one containing an anthracycline and CD20 directed therapy * Patients need to have radiographically documented disease Exclusion Criteria: * ECOG performance status ≥2. * Patients with active CNS disease * Pregnant or lactating women. Women and men of childbearing age should use effective contraception while on this study and continue for 1 year after all treatment is finished. * Impaired cardiac function (LVEF \<40%) as assessed by ECHO or MUGA scan. * Patients with the following cardiac conditions will be excluded: * New York Heart Association (NYHA) stage III or IV congestive heart failure * Myocardial infarction ≤6 months prior to enrollment * History of clinically significant ventricular arrhythmia or unexplained syncope, not believed to be vasovagal in nature or due to dehydration ≤6 months prior to enrollment * Patients with HIV or active hepatitis B or hepatitis C infection are ineligible. * Patients with prior allogeneic hematopoietic stem cell transplant are eligible, if more than 3 months from transplant and if patients have no active graft versus host disease (GvHD) and not on systemic immunosuppressive therapy. * Prior CD19-directed therapy including CD19 CAR T cells is allowed, as long as expression of CD19 is confirmed by flow cytometry or immunohistochemistry. * Patients with uncontrolled systemic fungal, bacterial, viral or other infection are ineligible. * Patients with any concurrent active malignancies as defined by malignancies requiring any therapy other than expectant observation or hormonal therapy, with the exception of squamous and basal cell carcinoma of the skin. * Patients with presence of clinically significant neurological disorders such as epilepsy, generalized seizure disorder, severe brain injuries are ineligible. * Any other issue which, in the opinion of the treating physician, would make the patient ineligible for the study.